{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V76OQNEN6LNGKFHKNJYBP3ITX7","short_pith_number":"pith:V76OQNEN","canonical_record":{"source":{"id":"1705.01212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T01:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"3ef00166b73b0681fc3fa10d8d88cb47805f840e98190259b2c1b1203e9a2c7e","abstract_canon_sha256":"e84cd88cb6e68fe295ae7842c2dc1b8d2da2bad7c01334babab2b4502664f171"},"schema_version":"1.0"},"canonical_sha256":"affce8348df2da6514ea6a7017ed13bfce39ee4e03b10218ae784d6f7fca0e22","source":{"kind":"arxiv","id":"1705.01212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01212","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01212v1","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01212","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"V76OQNEN6LNG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V76OQNEN6LNGKFHK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V76OQNEN","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V76OQNEN6LNGKFHKNJYBP3ITX7","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T01:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"3ef00166b73b0681fc3fa10d8d88cb47805f840e98190259b2c1b1203e9a2c7e","abstract_canon_sha256":"e84cd88cb6e68fe295ae7842c2dc1b8d2da2bad7c01334babab2b4502664f171"},"schema_version":"1.0"},"canonical_sha256":"affce8348df2da6514ea6a7017ed13bfce39ee4e03b10218ae784d6f7fca0e22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:53.089129Z","signature_b64":"D3eMO53XW8KihZy6k6c41M5CLL54qLity8iZuw69m+CbhBQgwlJpGLUsG3ZGH8tizrcLS9ri7NPxpVsK63y1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"affce8348df2da6514ea6a7017ed13bfce39ee4e03b10218ae784d6f7fca0e22","last_reissued_at":"2026-05-18T00:38:53.088600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:53.088600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01212","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P+Gq+gdGj2pXg1Ji0Sv6zPoGaNkFFSVxjrIYgmyawdO2pqz3anmmJkryc6qdXKj5rdnmxdxmIsVnStmKya6PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:13:12.656198Z"},"content_sha256":"2293933caf4d686a552eb9702fe49fd8866505be41b12fdc93aa3ae054c7b07b","schema_version":"1.0","event_id":"sha256:2293933caf4d686a552eb9702fe49fd8866505be41b12fdc93aa3ae054c7b07b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V76OQNEN6LNGKFHKNJYBP3ITX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness and scattering for the Boltzmann equations: Soft potential with cut-off","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jin-Cheng Jiang, Lingbing He","submitted_at":"2017-05-03T01:01:12Z","abstract_excerpt":"We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model $\\gamma=2-N$ with initial data small in $L^N_{x,v}$ where $N=2,3$ is the dimension. The proof relies on the existing inhomogeneous Strichartz estimates for the kinetic equation by Ovcharov and convolution-like estimates for the gain term of the Boltzmann collision operator by Alonso, Carneiro and Gamba. The global dynamics of the solution is also characterized by showing that the small global solution scatters with respect to the kinetic transport operator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01212","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+Fv2P6RRqZLbuh2bZcnNCjOV/pC6nlorFo0r6T/2cV8Em/kiNGEbLtRWJPiv7f6nAjZhiuqrvkvF8P9qhRkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:13:12.656559Z"},"content_sha256":"5c71a0b643cdf775454c54119fa62a3357c496654a3d7cc64804e771ecdcd0cb","schema_version":"1.0","event_id":"sha256:5c71a0b643cdf775454c54119fa62a3357c496654a3d7cc64804e771ecdcd0cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/bundle.json","state_url":"https://pith.science/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T23:13:12Z","links":{"resolver":"https://pith.science/pith/V76OQNEN6LNGKFHKNJYBP3ITX7","bundle":"https://pith.science/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/bundle.json","state":"https://pith.science/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V76OQNEN6LNGKFHKNJYBP3ITX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V76OQNEN6LNGKFHKNJYBP3ITX7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e84cd88cb6e68fe295ae7842c2dc1b8d2da2bad7c01334babab2b4502664f171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T01:01:12Z","title_canon_sha256":"3ef00166b73b0681fc3fa10d8d88cb47805f840e98190259b2c1b1203e9a2c7e"},"schema_version":"1.0","source":{"id":"1705.01212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01212","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01212v1","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01212","created_at":"2026-05-18T00:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"V76OQNEN6LNG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V76OQNEN6LNGKFHK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V76OQNEN","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c71a0b643cdf775454c54119fa62a3357c496654a3d7cc64804e771ecdcd0cb","target":"graph","created_at":"2026-05-18T00:38:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model $\\gamma=2-N$ with initial data small in $L^N_{x,v}$ where $N=2,3$ is the dimension. The proof relies on the existing inhomogeneous Strichartz estimates for the kinetic equation by Ovcharov and convolution-like estimates for the gain term of the Boltzmann collision operator by Alonso, Carneiro and Gamba. The global dynamics of the solution is also characterized by showing that the small global solution scatters with respect to the kinetic transport operator","authors_text":"Jin-Cheng Jiang, Lingbing He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T01:01:12Z","title":"Well-posedness and scattering for the Boltzmann equations: Soft potential with cut-off"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01212","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2293933caf4d686a552eb9702fe49fd8866505be41b12fdc93aa3ae054c7b07b","target":"record","created_at":"2026-05-18T00:38:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e84cd88cb6e68fe295ae7842c2dc1b8d2da2bad7c01334babab2b4502664f171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T01:01:12Z","title_canon_sha256":"3ef00166b73b0681fc3fa10d8d88cb47805f840e98190259b2c1b1203e9a2c7e"},"schema_version":"1.0","source":{"id":"1705.01212","kind":"arxiv","version":1}},"canonical_sha256":"affce8348df2da6514ea6a7017ed13bfce39ee4e03b10218ae784d6f7fca0e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"affce8348df2da6514ea6a7017ed13bfce39ee4e03b10218ae784d6f7fca0e22","first_computed_at":"2026-05-18T00:38:53.088600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:53.088600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D3eMO53XW8KihZy6k6c41M5CLL54qLity8iZuw69m+CbhBQgwlJpGLUsG3ZGH8tizrcLS9ri7NPxpVsK63y1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:53.089129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2293933caf4d686a552eb9702fe49fd8866505be41b12fdc93aa3ae054c7b07b","sha256:5c71a0b643cdf775454c54119fa62a3357c496654a3d7cc64804e771ecdcd0cb"],"state_sha256":"808648f006a1b5e8a6432b3cb62252e99fceb3b30f7257258c97afc5d1929470"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3rMmrYwlQTii8hdEHrbLBCCr7P5rhBVrmJ9K5bI2I3ZjgGmAo3IesQF/qSpL9t5JYxRa5aCmly0FIJaZjxQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:13:12.658458Z","bundle_sha256":"f4de98a2c3f25f904d4fac434488addef134659f344b974f5b9f827561f8d062"}}